Quantifying Ground Ice in Tien Shan and Pamir Permafrost: A Comprehensive Petrophysical Joint Inversion Study Applying the electrical Geometric Mean Model 

Abstract

Central Asian Mountain regions (Tien Shan and Pamir) are expected to be significantly impacted by climate change, affecting water availability and natural hazards. The cryosphere plays a crucial role in many watersheds of the region by providing water for hydropower station, irrigation, and domestic use downstream. At the same time, retreating glaciers and thawing permafrost increase the risk of natural hazards. Therefore, cryosphere monitoring systems are necessary to provide baseline data for estimating future water availability and detecting dangerous hazard zones. Despite the large areas underlain by permafrost in the Tien Shan and Pamir Mountain ranges, data on permafrost distribution, characteristics and evolution are scarce. However, quantitative estimations of permafrost subsurface components, especially water and ice contents, are needed to evaluate the consequences of current climate change on mountain permafrost environments. Recent field-based investigations have emphasised the coupled use of geophysical techniques, e.g., by employing the Petrophysical Joint Inversion scheme (PJI, Wagner et al., 2019) that combines electrical resistivity and seismic refraction p-wave velocity data to estimate the four phases present in the subsurface (volumetric contents of air, water, ice, and rock). The traditional PJI implementation relies on Archie’s law (Archie, 1942) as one of the primary petrophysical equation to link resistivity to porosity and water content. Archie's law is generally considered valid when electrolytic conduction dominates, a condition that is not universally justified for dry and coarse blocky substrates and landforms in mountainous terrain. Recognizing this limitation, Mollaret et al. (2020) introduced the electrical Geometric Mean Model as an alternative implementation in the PJI. The Geometric Mean Model  assumes random distributions of the four phases and offers the advantage of including the fractions of ice and air in the petrophysical equation for resistivity, which are not present in Archie’s law. In this study, we assess the feasibility and effectiveness of using the Geometric Mean Model within the PJI framework across an extensive geophysical dataset comprising 22 profiles in Central Asia (Kyrgyzstan and Tajikistan). Our research encompasses diverse landforms, including moraines, rock glaciers, talus slopes, and fine-grained sediments. Our goals are to (i) evaluate the performance of the Geometric Mean Model in comparison to Archies law across different landforms and (ii) address the existing data gap concerning mountain permafrost and ground ice contents in the Central Asian region.